LAMINAR LIQUID-LIQUID DISPERSION IN SMX STATIC MIXER

STUDY OF LIQUID-LIQUID DISPERSION OF HIGH VISCOSITY FLUIDS IN SMX

STATIC MIXER IN THE LAMINAR REGIME

By

MAINAK DAS, B.Sc. Eng.

A Thesis

Submitted to the School of Graduate Studies

in Partial Fulfillment of the Requirements

for the Degree

Master of Applied Science

McMaster University

©Copyright by Mainak Das, September 2011

ii

MASTER OF APPLIED SCIENCE (2011) McMaster University

(Chemical Engineering) Hamilton, Ontario

TITLE: Study of Liquid-Liquid Dispersion of High Viscosity

Fluids in SMX Static Mixer in the Laminar Regime

AUTHOR: Mainak Das, B.Sc.Eng. (University of Alberta)

SUPERVISORS: Dr. Andrew N. Hrymak and Dr. Malcolm H.I. Baird

NUMBER OF PAGES: xiii, 67, A4, B3

iii

Abstract

In this research, liquid-liquid dispersion of viscous fluids was studied in an

SMX static mixer in the laminar regime. Backlighting technique was used for

flow visualization, and the Hough transform for circle detection was used in

OpenCV to automatically detect and measure drop diameters for obtaining the

size distribution. Silicone oil and an aqueous solution of high fructose corn syrup

were used for dispersed and continuous phases respectively, and sodium

dodecyl sulfate was used as the surfactant to modify the interfacial tension.

Experiments were conducted at varying viscosity ratios and flow rates-each at

zero, low (~200 ppm) and high (~1000 ppm) surfactant concentrations. The

effect of holdup was explored only for a few cases, but it was found to have a

minimal effect on the weighted average diameter D43.

It was found that the superficial velocity and the continuous phase

viscosity had a dominant effect on D43. The tail at the higher end of the droplet

size distribution decreased with increasing superficial velocity and continuous

phase viscosities. It was also found that D43 decreased with lowering of the

interfacial tension. Furthermore, the effect of the dispersed phase viscosity was

significant only at non zero surfactant concentrations.

An approximate model has been proposed that relates D43 to the capillary

number. It is based on an energy analysis of the work done by the viscous and

iv

surface forces on a drop of an initial diameter that is largely determined by the

gap distance between the cross bars in the element.

v

Acknowledgements

I would like to sincerely express my gratitude to Dr. Hrymak and Dr. Baird

for giving me this learning opportunity and guiding me throughout this project.

Their commitment to the success of this research and innovative problem solving

approaches has been truly inspirational.

I would like to thank Paul Gatt and Dan Wright for helping with

equipment setup and troubleshooting. Their on-demand help made it possible

to finish this project on time. I would also like to thank Justyna Derkach for

providing guidance and assistance with lab safety.

My sincere thanks goes to Dr. Pelton`s group (especially Yuguo Cui) for

providing access to their equipments. Also, I would like to thank my colleagues

and friends for exchanging valuable information.

I would also like to acknowledge the financial support from the

Department of Chemical Engineering and School of Graduate Studies by

providing scholarships and teaching assistantships. I am also grateful to Proctor

& Gamble for funding this project.

Lastly, I would like to thank my parents and other family members for

their encouragement and constant support.

vi

Table of Contents

Abstract iii

Acknowledgements v

Table of Contents vi

List of Figures viii

List of Tables xi

Nomenclature xii

1. Introduction 1

2. Literature Review 5

2.1 Drop breakup 5

2.2 Correlations in the laminar regime 11

2.3 Correlations in the turbulent regime 15

2.4 Automated droplet detection 19

3. Experimental 25

3.1 Fluids used 25

3.2 Experimental rig and procedure 26

3.3 Flow visualization setup and image capture 31

vii

3.4 Image processing and circle detection 32

3.5 Note on measurement errors 38

4. Results and Discussion 40

4.1 D43 trends 40

4.2 Dmax trends 47

4.3 Droplet size distribution trends 49

4.4 Qualitative Images 55

5. Conclusion 62

5.1 Summary 62

5.2 Recommendations for future work 64

References 65

Appendix A A1

Appendix B B1

viii

List of Figures

Figure 1. Stability curves relating critical capillary number

with the viscosity ratio 6

Figure 2. Critical Capillary number as a function of viscosity ratio for three

different values of 8

Figure 3. Drop breakup modes in shear flow 9

Figure 4. Break up modes 10

Figure 5. Effective shear rate for SMX and Kenics mixe 13

Figure 6. 3D parameter space in standard Hough Transform for

circle detection 21

Figure 7. Two stage Hough transform illustration 22

Figure 8. Voting window 23

Figure 9. Process flow diagram with instrumentation 28

Figure 10. Entry configurations for continuous and dispersed phases 30

Figure 11. Flow visualization setup 32

Figure 12. Flow chart for image processing code 33

Figure 13. Sample raw image 34

Figure 14. Image after Bilateral Smoothing 35

Figure 15. Binary image after Canny Edge detection 36

Figure 16. Identified droplets 37

ix

Figure 17. Log-log plot to show the effect of interfacial tension

and viscosity ratio on D43 for c ~25 mPaS 41


and viscosity ratio on D43 for c ~70mPaS 42


and viscosity ratio on D43 for c ~200 mPaS 42

Figure 20. Log-log plot to show the effect of viscosity ratio on D43 at zero

surfactant concentration 44

Figure 21. Log-log plot to show the effect of viscosity ratio on D43 at low


Figure 22. Log-log plot to show the effect of viscosity ratio on D43 at high


Figure 23. Effect of number of elements on D43 46

Figure 24. Effect of interfacial tension and viscosity ratio on Dmax

for c ~25 mPaS 47


for c ~70 mPaS 48


for c ~200 mPaS 48

Figure 27. Image showing the breakup of a dispersed phase stream into drops as

it is passes through the gap between the cross bars 56

x

Figure 28. Image sequence showing drop breakup from impact with cross-points

of the packing 56

Figure 29. Image sequence showing a single drop breakup at cross-point 57

Figure 30. Model assessment by correlating D43 with capillary number 60

xi

List of Tables

Table 1. Correlations for droplet diameter in static mixers

in the turbulent regime 18

Table 2. Properties of fluids used in experiments 25

Table 3. Relative errors of measured and calculated values 38

Table 4. Droplet size distribution trends at zero surfactant concentration 50

Table 5. Droplet Size Distribution Trends at High Surfactant Concentration 53

xii

Nomenclature

Ca capillary number

Cacrit critical capillary number

CoV coefficient of variation

D mixer diameter, m

D0 drop primary diameter, m

D16 diameter below which 16% of the droplets lie in a distribution, m

D32 sauter mean diameter, m

D43 volume mean diameter, m



Df final droplet diameter after breakup of a primary drop, m

Di diameter of an individual drop in a distribution, m

Dmax maximum diameter, m

E overall energy, J

LT large turbulence scale, m

N number of droplets formed after break

n number of mixing elements

N0 number of droplets with an initial diameter D0

p viscosity ratio (dispersed to continuous phase)

Q volumetric flow rate, m3/s

r drop radius, m

xiii

Re Reynolds number

u superficial velocity, m/s

Vi viscosity group

Volmixer mixer volume, m3

We Weber number

P pressure drop across the mixer, Pa

Greek Letters

shear rate, s-1

flow parameter

power dissipation per unit mass, m2/s3

dispersed phase volume fraction

Kolmogorov scale, m

viscosity, Pa.S

density, kg/m3

interfacial tension, N/m

shear stress, Pa

Subscripts

c continuous phase

d dispersed phase

e emulsion

h hydraulic

p pore

M.A.Sc. Thesis - M. Das McMaster - Chemical Engineering

1

1. Introduction

Motionless mixers or static mixers have been in use since the 1970’s (Thakur

et al., 2003), and with time they have evolved to the point where they are now

found in a wide array of industries. These range from grain processing,

pharmaceuticals and cosmetics to petrochemicals, refining, and specialty

chemicals. They are used in continuous processes in both distributive and

dispersive mixing applications. In general static mixers are more energy efficient,

and among other applications, they are used instead of continuous stirred tanks

with rotating impellers for systems with relatively short residence times, plug

flow conditions and for blending or dispersing fluids that are sensitive to high

shear. They also become a more cost effective option for high pressure services.

These benefits are realized because of a static mixer’s mechanical simplicity and

compactness.

A typical static mixer contains a series of mechanical inserts- the number,

type and sequence of which are chosen to suit a particular application and to

optimize the mixing performance. These inserts can be broadly categorized to

have twisted- ribbon, plate and structured geometries. The twisted-ribbon type

is the earliest of static mixer internals, and is ideal for distributive mixing of low

viscosity fluids (such as gas-liquid dispersions) under turbulent conditions. Plate

type mixers are also used for applications in the turbulent flow regime, as these


2

designs create vortices. Structured packings have more complex geometry and

are often placed such that each cartridge is oriented 900 relative to its

neighbours. The most versatile in this category are the SMX (Sulzer, USA) and

SMXL, which have geometries with cross bars angled at 450 and 300 for SMX and

SMXL respectively. SMX- which is the subject of study in this thesis-is regarded

to be the best design choice for plug flow in tubular reactors, and for blending

and dispersing high viscosity fluids in the laminar flow regime (Paul et al., 2004,

p. 428).

In order to scale up static mixers reliably in liquid-liquid dispersion

applications, it is of prime importance to develop correlations or fundamental

models to predict key characteristics such as pressure drop, mean droplet size

and size distributions. The latter two are applicable to multi phase flow, which

complicates fluid dynamic studies because of fluid properties of multiple phases,

which includes interfacial tension. Such correlations and fundamental insights

also help to optimize the packing geometry for better performance. In liquid-

liquid dispersions with SMX packing for example, there is a strong drive from the

industry to eliminate the occurrence of oversized droplets in order to produce a

more uniform or narrower droplet size distribution. An appreciable amount of

numerical and experimental work has been done in this area, since the

fundamental contribution by Grace (1982). For example, Rauliene et al. (1998)

have done numerical investigations to characterize the extent of elongation flow


3

in various static mixers. Liu (2005) has done numerical and experimental studies

to study flow fields inside an SMX mixer. He also conducted numerical

simulations and experimental validations for single drop breakup in the laminar

regime (Liu et al., 2005). Direct investigations of droplet size distribution in SMX

mixers have been done by Legnard et al.(2001), Rao et al. (2007), Fradette et

al.(2007), Theron et al.(2010) and Das et al.(2005). Legnard and Felice studied

droplet dispersion in the turbulent regime and have based their correlations on

the classical Kolmogorov theory, whereas Fradette , Das and Rao have studied it

in the laminar regime. In all these studies, a major limiting factor was the

measurement of droplet size distribution. In most cases the measurement was

done using the micro encapsulation technique where the droplets were

hardened at the surface by means of interfacial polymerization. Rao et al. (2007)

and Fradette et al. (2007) used image/video capture and then manually counted

and measured the droplets to obtain a distribution. The latter technique,

because of the detailed measurements involved, imposes serious limitations on

the amount of data that can be acquired. Automating this process with computer

vision algorithms would have certainly helped the experimenters to conduct

more runs under different conditions, and come up with better correlations.

The research objective in this thesis is therefore is twofold. The first part will

be to leverage computer vision algorithms for automation and explore their

merits for rapid measurement of Droplet Size Distribution (DSD). The second


4

part will be to collect substantial data with the SMX elements in the laminar

regime under varying viscosity ratios, holdups and most importantly under

varying interfacial tension. Finally, this data will be used to study Droplet Size

Distribution (DSD) trends and to develop a model for correlating the variables

involved.


5

2. Literature Review

2.1 Drop breakup

In order to understand liquid-liquid dispersions in a mixer it is important

to understand the physics of drop breakup. Different breakup mechanisms

under different conditions can affect the maximum drop size and the nature of

the size distribution in a dispersion. The corollary of this fact is that the

identification of different size distributions (such as Gaussian, Log-normal,

bimodal etc) in a relatively less understood equipment can give an insight into

the flow conditions or breakup modes inside it.

A drop can break up as a result of the hydrodynamic forces around the

drop and/or as a result of collision with the internals of the mixer. When it

breaks up because of the hydrodynamic forces, the viscous shear stress from the

continuous phase exceeds the drop’s internal viscous and surface stresses.

Grace (1982) has done fundamental work in this regard with single drop breakup

experiments in steady simple shear and 2D extensional flow. He was able to

describe the breakup in terms of two dimensionless terms namely the capillary

number and the viscosity ratio. The capillary number in this case is defined as

(1)


6

where is the shear rate and r is the radius of the drop. This definition is also

synonymous with reduced shear rate (dimensionless shear rate). The viscosity

ratio is defined as the ratio of the dispersed phase viscosity to the continuous

phase viscosity and is given as

(2)

Figure 1 shows the relationship between the critical capillary number and

viscosity ratio

Figure 1. Stability curves relating critical capillary number with the viscosity ratio (data from Grace, 1982)

The drops break up when the capillary number exceeds a critical value. It

can be seen that for extensional flow the critical values are far lower than those

of simple shear, thus signifying that extensional flow is more efficient in breaking


7

drops. Depending on the mixer geometry, any degree of simple shear to

elongation flow is realizable. This is quantified by a flow parameter which is

defined as the ratio of the deformation (strain rate) to the rotational (vorticity)

component of the flow field and is given as

(3)

=0 for simple shear and =1 for purely extensional flow. Bentley and Leal

(1986) have used a computer controlled four roll mill to generate different types

of two dimensional flow. By being able to control the direction and speed of the

four rollers, they were able to set a desired ratio of the strain rate to the vorticity

components of the flow field in between the rollers, thereby producing

intermediary values of between zero and one). Figure 2 shows the critical

capillary curves for values of purely extensional), simple shear)


8

Figure 2. Critical Capillary number as a function of viscosity ratio for three different values of (after data Bentley and Leal ,1986)

It is also important to consider the effects of breakup in transient conditions.

Rauline et.al (1998) has shown with his numerical investigation that the flow

parameter changes along the length of a SMX static mixer. Hence a drop

experiences a transient flow field inside the mixer. Stone and Leal (1989) studied

the effects of transient conditions and found that by combining and altering the

flow types the drop can break at capillary numbers which are lower than the

critical values at steady conditions.

The modes of drop breakup depend on the viscosity ratio, surfactant

concentration, capillary number and flow conditions. The four typical modes are

necking, tip streaming, end-pinching and capillary instability. Figure 3 shows

where some of these modes occur in a simple shear flow


9

Figure 3. Drop breakup modes in shear flow (from Tucker and Moldenaers, 2003)

When the viscosity ratio, p is ≈1, the drop narrows at the center, assumes a

dumbbell shape and ultimately breaks into two mother drops with a few

daughters in between. Tip streaming occurs when p<1, and daughter droplets

are released from the tips. This type of breakup typically gives rise to a log-

normal distribution. When the capillary number far exceeds the critical value the

drop stretches, orients itself in the direction of the flow and breaks up because

of capillary wave instability. The effect of surfactant concentration on breakup

modes has been mentioned in Jansen (1997) and is shown in Figure 4. At low

surfactant concentrations, necking is predominant whereas tip streaming occurs

with higher surfactant concentration. This is because interfacial tension

gradients develop that cause unequal distribution of surface forces (de Bruijin,

1993).


10

Figure 4. Break up modes-a)narrowing waist breakup (no surfactant) b) one sided elongation (low-moderate surfactant conc.) c) narrowing waist with tip streaming (low surfactant conc.) d) highly-

asymmetric narrowing waist breakup (high surfactant conc.) (from Jansen, 1997)

Correlations of drop sizes in a liquid-liquid dispersion are usually done in

terms of the Sauter mean diameter, and is particularly useful when interfacial

mass transfer is being considered. The Sauter diameter is the ratio of the third

to second moment of the distribution and is given by

(4)

The measure D43 is also used in some correlations. It is the ratio of the fourth to

the third moments, and is referred to as the mass mean diameter. It is given by

(5)


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D43 places more emphasis on the larger drop sizes in the distribution. There are

also other measures such as D90, which is the diameter greater than 90% of the

droplets in a sample.

Other correlations are given in terms of coefficient of variation or CoV. It

is defined as the ratio of standard deviation to the mean of a sample size. It

gives an indication of the spread of the DSD. For a Gaussian distribution, which

can be inferred from a straight line in a cumulative frequency plot (Paul et al.

2004, pg. 677), the CoV is given as

(6)

where D84, D16 and D50 are defined similarly as D90.

2.2 Correlations in the laminar regime

There have been a few experimental studies in dispersion with SMX static

mixer in the laminar regime. Streiff (1997) has obtained correlations to predict

maximum diameter (dmax) for viscosity ratio, p<1, in the laminar regime. He

correlated the critical capillary number with the relation-

(7)

Dmax can then be estimated from the definition of the capillary number-


12

(8)

The above equation is valid when the drop residence time in the mixer is twenty

times greater than the critical burst time obtained by Grace (1982) in 2D

extensional flow. The critical burst time is the minimum time that is needed to

sustain the critical shear rate (calculated using Cacrit from Fig. 1) for drop

breakup.

Fradette (2007) has done systematic experiments to study the effects of

dispersed phase concentration, number of elements and the energy input on the

average diameter. It was found –albeit with limited data-that the average drop

size varied exponentially as , and with the viscosity ratio with the

relation , where Davg is the mean of the distribution when plotted

with logarithm of the diameter as the random variable. The viscosity ratio

ranged between 5-200, and the dispersed phase concentration (or holdup) -

defined as

(9)

ranged from 5-25%. Furthermore, to characterize the performance of SMX

mixer, the effective shear rate -given as


13

(10)

-was compared (shown in Figure 5) and was found to be higher than that of

Kenics mixer for a given overall energy (Karbstein and Schubert, 2005)given by

(11)

where P is the pressure drop in the mixer and Vmixer is the total volume of the

mixer. The critical capillary number, Cacrit, in Eq (10) is assumed to be constant

and is obtained from the chart for extensional flow given in Figure 2. It was

assumed constant because flow within SMX was largely assumed to be of the

extensional type. This assumption is however, not accurate as shown by

experiments in Liu (2005).

Figure 5. Effective shear rate for SMX and Kenics mixer (from Fradette, 2007)


14

The approach of Das et al. (2004) was to treat elements of the mixer as a

bundle of narrow pores. The drop breakage was assumed to occur in the

boundary layer within the pore with a strain rate of

(12)

where up is the average velocity in the pore and Dp is the pore diameter. With

appropriate choice of Dp and up, and with an assumed critical capillary number,

the droplet diameter (maximum stable diameter) could be estimated using non-

dimensionless terms :

(13)

where Vip is the pore viscosity number defined as

(14)

The emulsion viscosity (e) is considered here instead of the continuous phase

viscosity, and is a function of the dispersed phase fraction. The change in

apparent viscosity of the continuous phase has also been observed by Fradette

(2007). With a similar approach, another equation was derived for intermediate

Reynolds number(20<Rep<350) by considering the inertial forces that-unlike in

laminar creeping flow- were assumed to have dominance over the viscous shear

forces The relation in this case was derived as-


15

(15)

where Wep is the pore Weber number. Experimental data collected to validate

the above models were limited , showed some scatter , and also deviated from

values as predicted by the models.

Rao et.al (2004) derived a model assuming that a small drop would collide

and attach to the packing and grow until the drag forces from the continuous

phase would become large enough to detach it. The model is shown in the

equation below-

(16)

where kd is a constant. The inertial and surface forces were considered to be

negligible. The model might be of relevance in a situation where the dispersed

phase wets the packing material.

2.3 Correlations in the turbulent regime

Many droplet size correlations have been developed for the turbulent

regime in SMX static mixers. They are based on Kolmogorov theory of isotropic

turbulence. A droplet is assumed to breakup in eddies with length scales smaller

than the droplet diameter. These scales are somewhere in between the large

(primary) turbulence scale and the Kolmogorov microscale (Paul et al., 2004, pg.

657), given by


16

(17)

where is the power dissipation per unit mass. The energy spectrum density in

this range is given by

(18)

The shear stress to break up the drop is given by

(19)

for low dispersed phase viscosities, this result translates to the following relation

(20)

where,

(21)

The above relation is equivalent to

(22)

where We is the Weber number-a dimensionless number, which is a ratio of the

inertial to surface forces. Most correlations in the turbulent regime are based on

Eq (22), and have been modified to account for dispersed phase viscosity, friction

factor (Middleman, 1974), number of elements etc. These correlations have


17

been summarized for Kenics and SMX mixers in Table 1. Middleman (1974),

Berkman and Calabrese (1988), and Theron et al. (2010), have used the

superficial velocity, and hence the Weber number in their correlations is given

as-

(23)

Streiff et al. (1997) used a hydraulic diameter and interstitial velocity instead of

the mixer diameter and superficial velocity. Legnard et al. (2001) used a pore

diameter and pore superficial velocity, by considering the mixer elements as a

bundle of cylindrical pores. Both the hydraulic and pore diameters are

dependent on the type of the mixer. The Weber numbers Weh and Wec, are

defined analogously to Eq (23). Furthermore, to take into account the dispersed

phase viscosity d, Berkman and Calabrese (1988) have introduced the viscosity

group given as

(24)


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Table 1. Correlations for droplet diameter in static mixers in the turbulent regime

Author Mixer Type

Correlation Dispersed phase vol. fraction range

Middleman (1974) Kenics

Streiff et al. (1977) SMV

Berkman and Calabrese (1988) Kenics

Legnard et al. (2001) SMX

Theron et al. (2010) SMX

,

is the number of elements


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2.4 Automated droplet detection and measurement

There are two classes of algorithms for pattern recognition in an image:

local and global processing methods. Local processing algorithms look for

patterns in a specified area of an image, whereas in global approaches, the entire

image is considered at a time to detect shapes or patterns. In one type of local

processing algorithm for example, an edge pixel (discontinuity in brightness

intensity) in a binary image is linked with adjacent pixels with pre-defined

criteria. Such a method was used by Kim and Lee (1990) to detect and measure

droplets from a spray nozzle. Pixels were grouped together based on rules, and

classified (based on simple patterns) either as potential drops or foreign objects.

The group of connected pixels were then measured for the diameter. One major

drawback of their algorithm is that it is incapable of detecting overlapping drops,

and is very sensitive to noise-in the binary image.

The Hough Transform (Bradski and Kaehler, 2008, pg. 153) is a global

processing algorithm, which has been gaining popularity for line and circle

detection applications. It has been used in disciplines ranging from

oceanography to microbiology, and is also used for pupil/iris detection and

tracking. It has an advantage over other algorithms because it can detect and

measure circles simultaneously, is capable of detecting overlapping circles and is

more robust for noisy images. In essence, it is a voting algorithm whereby an

edge pixel in a binary image is used to vote for all possible circles or lines that it


20

could belong to. To illustrate this, we consider a circle represented by the

equation

(25)

where the coordinates of the centre (a,b) and the radius r, are parameters that

completely define the circle. An edge pixel can therefore be used to compute all

possible (a,b,r) values in the parameter space, and vote for these parameter

triplets in a 3D accumulator array. A ``vote`` is typically implemented by

incrementing the value in the cell of the array by one. From a geometrical

standpoint, the standard Hough transform algorithm votes for all the points on a

right circular cone that emanates from the edge pixel. The concept is

schematically shown in Figure 6. If a set of edge pixels are indeed a part of a

circle, then the parameters (a,b,r) corresponding to that circle will receive more

votes than its neighbouring points in the 3D accumulator array. The final step in

the algorithm is therefore to find local maxima in the accumulator array and

mark detected circles.


21

Figure 6. 3D parameter space in standard Hough Transform for circle detection (from Yuen et al. 1990)

This standard Hough transform algorithm has an inherent disadvantage because

the 3D accumulator array demands more memory and also computational time

for searching for local peaks within it. Furthermore, the accumulator grows only

larger as the range of radii increases.

Many optimized versions of this algorithm have been developed to

increase the computational efficiency. Yuen et al. (1990) did a comparative

study on different variants of the algorithm, and concluded that the Gerig Hough

Transform with gradient (GHTG) and 2 stage Hough transform (2HT) have the

best combination of accuracy and efficiency. 2HT has been adopted in standard

freely available libraries such as OpenCV. In the first stage of 2HT, the voting is

done only along the direction of the edge gradient. This requires only a 2D

accumulator array, and because the centre of a circle lies along the direction of

the gradient, the centres are found by finding the local maxima in the


22

accumulator array. In the second stage, for each centre found, distances to edge

pixels within a specified radius are computed. A radius histogram is then

constructed for that candidate centre, wherein a peak would identify the most

probable radius . The pictorial representation of 2 HT is shown in figure 7.

Figure 7 a) first stage 2D accumulator array to find centres b) histogram for a given candidate centre to find the radius in the second stage (from Yuen et al. 1990)

The Hough transform has been used very recently by Bras et al. (2009) to

automate DSD measurement for liquid-liquid dispersions in a stirred

mixer/settler device. To reduce the number of noise votes, the edge gradient

information was also used to vote in only two sections of the right circular cone

in the 3D accumulator. This is shown in Figure 8.


23

Figure 8 Voting window (Bras et al., 2009)

Brás et al. (2009) also found that the algorithm is susceptible to detecting false

droplets when the image quality is poor. This is because poor quality images can

cause more noisy edges (erroneously detected edges), which results in more

noise votes. It also leads to erroneous computations of edge gradient directions.

Therefore, to quantify the performance of the algorithm they used two metrics,

which are defined as follows-

(26)

(27)

where TP, FP and FN stand for true positives, false positive and false negatives

respectively. In an ideal case both recall and precision should be 100 %.

However, in a typical case there is a trade off between these two metrics. Bras

et al. (2009), saw their recall and precision varying from 90% to 50 % , depending


24

on the quality of the image. Hence, while using this algorithm it is imperative

that the drops in the image be in sharp focus with minimal motion blur.


25

3. Experimental

3.1 Fluids used

Silicone oil was used as the dispersed phase and an aqueous solution of

High Fructose Corn Syrup (HFCS) was used for the continuous phase. The

silicone oil used was Xiameter-PMX200 silicone fluids from Dow Corning, and the

HFCS was supplied by UNIVAR Canada. The properties of the fluids are given in

Table 2. Because of limited accuracy in measuring large volumes, and due to the

non linear behaviour of HFCS viscosity with dilution, it was difficult to prepare an

exact HFCS solution. Hence the actual viscosities were measured every time

after a HFCS solution was prepared. They differed slightly with the values given

in table 2, and have been included in the data table in appendix A. The viscosity

was measured by the Brookfield Viscometer (using spindle #1) and verified with

Zahn Cups measurements. All viscosity measurements were carried out at room

temperature of 210C.

Table 2. Properties of fluids used in experiments

HFCS Soln. (90%)

HFCS Soln. (80%)

HFCS Soln. (70%)

Silicone Oil (500 CSt.)

Silicone Oil (1000 CSt.)

density3 (kg/m3) 1360 1320 1280 978 978

viscosity (mPaS) 200 70 25 489 978

Sodium dodecyl sulphate (SDS) was used as the surfactant, to lower the

interfacial tension. The critical micelle concentration (CMC) of SDS in pure water


26

at 250C is 0.0082 M (Mukherjee and Mysels, 1971), which corresponds to 2365

ppm. The experiments were carried out below this concentration-starting from

zero, low (~200 ppm), and then finally at high (~ 1000 ppm) concentration levels.

The interfacial tensions corresponding to these three levels were 40, 20 and 12

mN/m respectively. A fresh batch of HFCS solution was made between each

surfactant concentration level. The actual interfacial tension was measured for

every batch after surfactant addition to ensure that it was close to the

aforementioned values.

The interfacial tension measurements were done using the pendant drop

method with the DSA10 unit from Kruss, Germany. This device is typically used

to measure the surface tension at the liquid-air interface. However, in this case

the interfacial tension at the liquid-liquid interface was measured using a

transparent acrylic cuvette, which was filled with silicone oil. The heavier HFCS

solution was used for the drop phase, and the drop was created inside the

surrounding silicone oil. Since the cuvette was transparent, the drops were

imaged and the interfacial tension values were reported by the software based

on the analysis of the drop shape.

3.2 Experimental rig and procedure

A schematic of the experimental rig with relevant instrumentation is

shown in figure 9. The static mixer used is made of acrylic, and is surrounded by


27

a mineral-oil filled light box to correct for the refractive distortion caused by the

curvature of the inner cylindrical surface. The mixer’s inner diameter is 41.18

mm and its height is 92 cm. A smaller mixer with a diameter of 15.75 mm was

also used, but because of time constraints only limited runs were obtained.

Plastic shims support the SMX inserts which fit snugly inside the column. These

SMX elements are made of titanium and have the same geometry as described in

Rao et. al (2007). They have a L/D ratio of one with a void fraction of 0.892, and

are arranged in the conventional form with each element oriented 90o with

respect to its adjacent ones.


28

Figure 9. Process flow diagram with instrumentation

CW HEX

SMX Static

Mixer

Continuous

Phase Tank Dispersed

Phase Tank

Receiving

Tank

Separating

Tank

CW HEX

FTTG

FT TGPG PG

2 HP Gear

Pump

2 HP Gear

Pump

VFD VFD

I/O

card

PC with

control

software


29

A 15 gallon (57 L) tank was used for the continuous phase to allow for

enough run time to capture images at flow rates of up to 10 L/min. Flowserve

rotary gear pumps (model no: 2GA) were used for both continuous and

dispersed phase sides. These were run by 2 HP AC motors, which were

controlled by a Variable Frequency Drive (VFD) that received frequency as an

input from the PC. Omega positive displacement flowmeters (FPD1002B-A)

were used to measure the volumetric flow rates. The flow rates were displayed

on the monitor, and were manually controlled by changing the input frequency

to the VFD, which ultimately changed the RPM of the motor. Recirculation lines

were used to relieve system of backpressure, to homogenize the continuous

phase after dilution and to clean the system. Heat exchangers were used only

with high viscosity fluids and at high flow rates to maintain the operating

temperature of 21o C. For most runs they were on standby as the temperature

on the thermometer did not show signs of temperature rise due to viscous

dissipation. As shown in figure 10, two entry configurations were used for the

static mixer. Continuous phase entered from the bottom centre of the mixer

when it was at high viscosity (~200 mPaS) to allow the development for fully

developed laminar flow. For the other two viscosity levels (70 and 25 mPaS),

the continuous phase entered from the side through an L-shaped tube while the

dispersed phase entered from the bottom.


30

In a typical run, the continuous phase pump would first be started and

brought to a desired flow rate. The dispersed phase pump would then be

started for a set flow rate that would achieve a desired holdup . The dispersion

would then be captured by the flow visualization setup (described below). The

liquids would separate in the separating tank, with the heavier cont. phase

settling at the bottom. The continuous phase would then be drained and

transported manually to the continuous phase tank for reuse. Since the silicone

oil was bought in bulk and was the minor phase, it was seldom reused.

Especially, for the low and high surfactant concentration levels, silicone oil was

never used for more than one pass through the system. Surfactant build-up in

the silicone oil phase was therefore avoided.

Figure 10. Entry configurations for continuous and dispersed phase:a) continuous phase (70 and 25 mPaS) entering from the side and dispersed phase entering from the bottom, b) continuous phase (200 mPaS)

entering from the bottom and dispersed phase entering from the side (from Rao et al.,2007)


31

3.3 Flow visualization setup and image capture

Simple backlighting technique was selected for flow visualization (shown

in figure 11). The light source was a 2000 lumens fluorescent white light bulb

with a diffuser attached to the exterior of the mixer at the light end. At the

other end, a Navitar 4X zoom lens was used with a Pixelfly QE camera, which is

capable of capturing 1280x1024 images at 12 frames per second. The camera

and the lens were placed on a manually controlled x-y-z positioner to precisely

control the field of view and the focal plane. The plane closest to the wall was

selected as the focal plane in order to minimize the possibility of out of focus

droplets at the front of the plane obscuring the ones in it. The depth of field for

the lens was determined to be 3 mm, and hence only the droplets within the first

3mm from the inner wall of the mixer were captured. The field of view was set

about four inches from the top element.

For a typical run, a sample of 200 images was taken. This was

determined to be sufficient as the number of droplets captured was enough for

the mean and standard deviation to converge. The images were taken at a

frequency such that the time period exceeded the time taken for a drop to pass

through the field of view. PCO camware software was used to trigger the image

capture and to handle the sequence of images. A 0.001 s exposure time was

used for all images.


32

Figure 11. Flow Visualization Setup

3.4 Image processing and circle detection

The flowchart in figure 12 summarizes the code-in appendix B- that was

used for image processing and circle detection. It was coded in C++ , with the

OpenCV library of functions, which were used for each of the blocks in the flow

chart. The functionality and the parameters of these functions are documented

in Bradski & Kaehler (2008).


33

Figure 12. Flow chart for image processing code

In the pre-processsing steps an image first goes through bilateral smoothing.

This is an edge preserving smoothing technique that is used to filter the high

frequency noise in the image. It is akin to Gaussian smoothing, except in this

case an additional parameter is used to specify the variance of the Gaussian filter

in the colour domain. It then goes through Canny edge detection routine

(described in Bradski & Kaehler (2008), pg. 151), where a gradient threshold is

used as a parameter to ignore the edges that are less prominent. These edges

would correspond to out of focus drops. The gradient threshold, therefore, is a

key parameter that determines the tolerance to out of focus drops that lie

outside the focal plane. Figures 13-15 illustrate the effect of these pre-

processing steps for a sample raw image.


34

Figure 13. Sample raw image


35

Figure 14. Effect of Bilateral Smoothing (edge preserving algorithm)-image is blurred except at the edges, which are still preserved

The binary image from the Canny edge detection routine is then used for the

Hough circle algorithm that uses the 21-HT version (as described in literature

review) of the algorithm. The source code for this function was slightly modified

to improve the edge gradient direction calculated from Sobel derivatives. An

important parameter in the Hough circle routine is the


36

Figure 15. Binary image after Canny Edge detection

accumulator threshold, which determines the minimum number of votes that is

required in order to be included in the local maxima detection in the 2D-array.

Since the number of votes is directly proportional to the radius of the circle, the

function has to be called multiple times depending on the range of radii. This is

because for large radii range, the accumulator threshold either becomes too low

for large radii, or too high for small radii, which in turn respectively increases the

propensity of exclusion of smaller droplets or false detection of large droplets. In

this case, the function was called upon separately each for two groups of radii,

and the optimum threshold was determined on a trial an error basis. Figure 16


37

shows the circles detected by the Hough circle routine for the sample raw image.

The recall and precision for this sample image are both 100%.

Figure 16. Identified Droplets

There are a few salient points on the overall performance of the

algorithm that were seen during the entire course of experimentation. They are

as follows-

-Droplets less than 40 pixels in diameter were difficult to detect. This is because

the edges for small droplets (especially at high magnification) were not

prominent. Furthermore, the accumulator threshold for the group of small radii,

was set higher for radii < 20 pixels to qualify for local maxima detection


38

- The performance of the algorithm is sensitive to the quality of the images. At

high flow rates, the images taken were affected by motion blur and were not as

sharp as the sample image shown above. In these cases, the algorithm had

higher rates of false positives for radii ranging between 80-90 pixels. This

affected the distribution by introducing false peaks, and also affected D43 by

adding a small negative bias.

-The key parameters such as Canny edge threshold and the accumulator

threshold parameters had to be fine tuned for different image qualities. The

algorithm therefore cannot be considered as a plug and play function that would

work in all scenarios.

3.5 Note on measurement errors

Table 3 gives the relative errors of measured and calculated values.

Except for mass, volume and viscosity, the relative errors of other directly

measured quantities are based on observation.

Table 3. Relative errors of measured and calculated values

Quantity Relative error

volume, V ±5%

mass, m ±1%

density, ±6%

interfacial tension, ±10%

viscosity, ±1%

flow rate, Q ±5%

superficial velocity, u ±5%

capillary number, Ca ±16%

reynolds number, Re ±12%


39

Error estimate on D43 measurement can only be obtained by comparing

the true value to the measured values for a large number of data points.

Because a true value can only be obtained by manually measuring the drops,

such an exercise is infeasible given the scope of the research. We can however,

identify the sources of random and systematic errors. Sources of systematic

errors are-sampling near the wall of the mixer, limited resolution of the

algorithm to detect small droplets and the algorithm`s sensitivity to image

quality-which can cause a negative bias from false positives for poor quality

images. Random errors can be attributed to drops passing behind and in front of

the focal plane, which can cause changes in light intensity and visibility of drops

in the focal plane. These errors should be small when compared to the

systematic errors. Furthermore, because the algorithm process ~200 images

(~1000 droplets) to obtain a single D43 measurement, we obtain less variability in

measurement, and hence we can say that the algorithm is not significant source

of random error.


40

4. Results and Discussion

Appendix A contains the experimental data in tabulated form. The data were

mainly collected using the 41.18 mm diameter mixer. It was originally planned

to collect similar data with a smaller 15.75 mm diameter mixer, however due to

time constraints only a very limited number of runs was obtained.

It is to be noted that the effect of holdup (dispersed phase fraction) was

studied only for the case of no added surfactant, and only with continuous phase

viscosities of 25 and 70 mPa.S, and at certain flow rates. Since the effect was

minor, these points appear as clusters in the figures that follow. The rest of the

data sets were obtained at a constant holdup of 10%, while varying the

superficial velocity.

4.1 D43 trends

The D43 measure has been used instead of the Sauter mean diameter

(D32) because it places more emphasis on the larger size droplets and is therefore

better in this case as distributions from SMX mixers exhibit a significant tail.

Moreover, it is less sensitive to exclusion of smaller diameter droplets, and

hence is even more appropriate with the measurement system used, which has a

limited recall for smaller diameters.


41

Figures 17, 18 and 19 show the effect of interfacial tension on D43 for

continuous phase viscosities of 25, 70 and 200 mPaS respectively. The values of

D43 have been plotted against superficial velocity to simultaneously demonstrate

the effect of interfacial tension. Low (~200 ppm) and high (~1000 ppm)

surfactant concentrations correspond to interfacial tensions of 20 and 12 mN/m

respectively, and are represented by slashes and crosses on the markers

respectively.

Figure 17. Log-log plot to show the effect of interfacial tension and viscosity ratio on D43 for c ~25 mPaS (low and high surfactant conc. correspond to 200 and 1000 ppm respectively)


42

Figure 18. Log-log plot to show the effect of interfacial tension and viscosity ratio on D43 for c ~70mPaS

Figure 19. Log-log plot to show the effect of interfacial tension and viscosity ratio on D43 for c ~200 mPaS


43

From the plots above, it can be seen that D43 decreases by lowering the

interfacial tension. However, the effect is less apparent at low surfactant

concentration. It is known that surfactants have diffusion kinetics (Zhang et al.,

1999), and one can speculate that this discrepancy could arise because the

interfacial concentration at a moving surface is less than the equilibrium value,

which would result in interfacial tension being larger than the measured value.

Furthermore, it can be seen in Fig. 17 &18 that except for the zero surfactant

case, the D43s are higher for the high dispersed phase viscosity (1000 cst. oil) for

a specific paring with continuous phase viscosity. These observations, combined

with the clear effect of the superficial velocity, suggest that the drop breakup is a

function of the capillary number (Ca=cucd/) and the drop viscosity, which is

conventionally taken into account with the viscosity ratio.

Figures 20, 21 and 22 show the effect of viscosity ratio on D43 at different

surfactant concentration levels. The data is the same for the plots above, except

that they have been regrouped to illustrate the effects of viscosity ratio.


44

Figure 20. Log-log plot to show the effect of viscosity ratio on D43 at zero surfactant concentration (viscosity ratios arranged with respect to continuous phase viscosities- from 25 mPaS (squares) to 200 mPaS (triangle); black fill represents pairing with 1000 Cst. oil whereas no fill represents pairing with 500 Cst. oil)

0.3

3

0.01 0.10

D43

(mm

)

Superficial Velocity, ucd (m/sec)

Effect of viscosity ratio on D43 at zero surfactant concentration

p=19.6

p=36.22

p=7.0

p=12.5

p=4.3


45

Figure 21. Log-log plot to show the effect of viscosity ratio on D43 at low surfactant concentration

Figure 22. Log-log plot to show the effect of viscosity ratio on D43 at high surfactant concentration


46

From Figures 20-22, we see that D43 has a stronger correlation with the

continuous phase viscosity- more so than the viscosity ratio. The trend is very

consistent across all surfactant concentration levels, in that we see that D43

decreases with increasing continuous phase viscosity. However, for a specific

continuous phase viscosity, D43s are higher when paired with the 1000 cst. oil

than paired with the 500 cst. oil. Again the results indicate that hydrodynamic

and surface forces are at play here.

Figure 23 shows the effect of the number of elements on D43. The

numbers were varied between six and ten.

Figure 23. Effect of number of elements on D43


47

The values of D43 are consistently higher with six elements. Since the system is

dilute (), this observation cannot be attributed to drop coalescence. As

mentioned in Fradette et al. (2007), in addition to the nature of the flow field,

the residence time inside the mixer elements is very important. If the mean

residence time is less than the time required to break the drop then size

reduction may not be achieved. This phenomenon can also be modelled by the

equation given by Middleman (1974).

4.2 Dmax trends

Figures 24, 25 and 26 show the effect of Interfacial tension and superficial

velocity on Dmax, which is the maximum droplet size found in the distribution.

Figure 24. Effect of interfacial tension and viscosity ratio on Dmax for c ~25 mPaS


48




49

It can be seen that for low continuous phase viscosity and zero surfactant

concentration, Dmax is in the vicinity of 5 mm. Very limited data was also

obtained with a mixer diameter of 15.75 mm. Dmax values for these three runs

were approximately 1.5 mm. These two values are very close to the measured

gaps (5 mm and 1.5 mm respectively) between the cross bars for 41.18 and

15.75 mm diameter mixer elements. This observation suggests that there is

effectively a slicing action of the crossbars to determine the initial drop size. If

these drops are not broken any further, due to inadequate hydrodynamic forces

or residence times further up the mixer, then they appear as oversize drops in

the distribution. This “slicing” action is also shown in the section Qualitative

Images below.

4.3 Droplet size distribution trends

Table 4 compares the droplet size distributions at low and high superficial

velocities and at different viscosity ratios-all obtained at zero surfactant

concentration. The low values range from 1.5-2 L/min, whereas the high values

range from 6-8 L/min (Please see Appendix A for specific values for the given run

numbers).


50

Table 4. Droplet size distribution trends at zero surfactant concentration

Superficial Velocity

Low High

p=36.2

(c=27 mPaS,

d=978 mPaS)

p=19.6

(c=27 mPaS,

d=489 mPaS)

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 41

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 23


51


Low High

p=12.5

(c=78 mPaS,

d=978 mPaS)

p=4.3

(c=230 mPaS,

d=489 mPaS)

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 36

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 27

0%

2%

4%

6%

8%

10%

12%

14%

16%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 29


52

The general trend for these distributions is that the frequency of occurrence is

more or less the same (i.e. we see a plateau) in a specific diameter range. This is

followed by a tail that becomes smaller and narrower with increasing continuous

phase viscosity and superficial velocity. As explained in the previous section, it

can be inferred that for a given residence time inside the mixer, size reduction is

achieved as the hydrodynamic forces increase in relation to the interfacial forces.

For some runs-as in Run 38 for example-the distributions show a sharp cutoff in

the droplet size. This however, is a result of the Hough circle detection

algorithm’s propensity to detect false positives within a range (which in this case

is 2 mm) when the image quality is poor.

Table 5 compares the same, but at high surfactant concentration (~1000

ppm).


53

Table 5. Droplet Size Distribution Trends at High Surfactant Concentration


Low High

p=16.3

(c=60 mPaS,

d=978 mPaS)

p=8.2

(c=60 mPaS,

d=489 mPaS)

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 87

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 88

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 93

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6Fr

eq

ue

ncy

Diameter (mm)

DSD Run 95


54


Low High

p=4.3

(c=230 mPaS,

d=978 mPaS)

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 82

0%

2%

4%

6%

8%

10%

12%

14%

0 1 2 3 4 5 6

Fre

qu

en

cy

Diameter (mm)

DSD Run 84


55

We see that at high surfactant concentration the distributions tend to resemble

a log-normal distribution. It tends towards becoming a Gaussian (as in the case

with run 84), with increasing superficial velocity and continuous phase viscosity.

This could be because of a change in breakup mechanism as a result of the

addition of surfactant. A possible candidate for a dominant mechanism could be

tip streaming, since the breakup of a large number of daughter droplets from the

tip of a large mother droplet gives rise to a log-normal distribution. This

conjecture is further supported by Janssen (1997), wherein tip streaming has

been described as being more favourable with moderate surfactant

concentration.

4.4 Qualitative Images

Images were also taken inside the third element (from the bottom) of the

mixer. The purpose of this was to get a qualitative view of the drop breakup

mechanism inside the mixer. Figure 27 shows the breakup of a stream as it

passes through the gap between the crossbars. In figure 28, an image sequence

is shown that demonstrates the drop breakup from collision with cross -points as

described in Liu (2005) and shown in Figure 29.


56

Figure 27. A frame from an image sequence showing the breakup of a dispersed phase stream into drops as it is passes through the gap between the cross bars

Figure 28. Image sequence showing drop breakup from impact with cross-points of the packing


57

Figure 29. Image sequence showing a single drop breakup at cross-point (Liu, 2005)

From the images above, we can conclude that there are multiple breakup

mechanisms occurring inside the mixer. Furthermore, as seen in fig. 27, the

slicing mechanism is seen wherein the dispersed phase stream is stretched as it

passes through the gap between the cross bars, and ultimately breaks due the

extensional and compression regions in the surrounding three dimensional flow

field.

4.5 Proposed Model

An observation-based model has been proposed by Dr. Baird. A drop can

be said to breakup in a 2-stage process-

-The first stage is the initial formation of primary drops (with diameter D0), which

forms with the interaction with the packing. The diameter D0 is of the same

order of magnitude as the gap between the adjacent plates in the packing.


58

-Secondary drops with diameter, D<D0 are formed by a mechanism of viscous

shear as described in Janssen et al. (1997) and Christini et al. (2003). The final

distribution contains a few relatively large drops and a much larger number of

smaller ones.

We equate the work done by viscous shear with the increase in surface

energy owing to the size reduction from D0->Df. Consider a large number of N0

drops of diameter D0 undergoing breakup to diameter Df (<D0). Then by

continunity the number of drops N is given by

(28)

and the relative increase in surface area is given by

(29)

from eq (28) and (29), the above simplifies to

(30)

Therefore the increase in suface energy per single drop is given by

(31)


59

where is the interfacial tension.

Work done on the initial drop by viscous shear is proportional to

(32)

By assuming a shear rate of

, the proportionality above can be written as

(33)

Since the increase in surface energy is proportional to work done for

breakup we get,

(34)

which simplifies to

(35)

where Ca is the capillary number. Therefore D0, Df and Ca can be related by the

equation

(36)


60

where k is an unknown proportionality constant. However, we now have a basis

to plot the data. If we assume Df≈D43, then we can plot 1/D43 Vs Ca, where the

intercept would be 1/D0.

In Figure 29, 1/D43 has been plotted against where p is the

viscosity ratio . Since the dispersed phase viscosity has not been considered in

the above energy analysis, the capillary number has been multiplied by the

viscosity ratio to the nth power. The value of the exponent n that gives the best

linear fit has to be determined. Furthermore, since we suspect that the actual

interfacial tension is higher than the measured interfacial tension because of

diffusion kinetics, a reduction factor is used. It is the fraction of reduction of the

Figure 30. Model assessment by correlating D43 with capillary number

R² = 0.8784

0.00

0.50

1.00

1.50

2.00

2.50

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

D4

3-1

(mm

-1)

Ca*pn

Model assessment: correlation with capillary number and viscosity ratio

data with 41.18 mm dia.

data with 15.75 mm dia.


61

interfacial tension from zero surfactant to low or high surfactant concentration.

From Excel solver, the best values of n and the reduction factor were determined

to be -0.66 and 0.98 respectively. This gives a reasonably good fit with a R^2

value of 0.88. The trend line (for 41.18 mm dia.) intercepts the vertical axis at

approximately 0.25, which corresponds to D43 ≈4 mm. Although, the data set for

the 15.75 mm dia. is not large enough to substantiate any claim, however, it

does seem to intercept the y-axis at ~0.6 mm, which corresponds to a D43≈ 1.7

mm. Since both 4 mm and 1.7 mm are values that we might expect for D0, we

can say that the model is a good starting point. It might be improved by

considering the effect of internal resistance of the drop phase viscosity in the

energy analysis.


62

5. Conclusion

5.1 Summary

In this research, liquid-liquid dispersion of viscous fluids was studied in an

SMX static mixer in the laminar regime. Backlighting technique was used for

flow visualization, and Hough transform for circle detection was used in OpenCV

to automatically detect and measure drops for obtaining the size distribution.

Silicone oil and an aqueous solution of high fructose corn syrup were used for

dispersed and continuous phases respectively, and sodium dodecyl sulfate was

used as the surfactant to lower the interfacial tension. Experiments were

conducted at varying viscosity ratios and flow rates-each at zero, low and high

surfactant concentrations. The effect of holdup was explored only at specific

viscosity ratios and at certain flow rates, and it was found to have a minimal

effect on D43. Further observations made were the following-

Superficial velocity and continuous phase viscosity seemed to have a

dominant effect on D43. The effect of dispersed phase viscosity was

significant only at low and high surfactant concentrations.

There was a measurable decrease in D43 at low surfactant concentration,

and a significant decrease at high surfactant concentration. This

confirmed that there is an effect of interfacial tension.


63

Droplet size distributions typically were found to have a long and wide

tail, which became narrower and shorter with higher superficial

velocities, higher continuous phase viscosities, and lower interfacial

tension. For the lowest interfacial tension (high surfactant

concentration), the size distribution was log-normal.

The gap between cross bars (or adjacent plates) in the packing seemed to

determine a primary diameter, which appeared as Dmax in the absence

of major dispersion further up in the packing. This observation is

consistent with Catalfamo et al. (2003), whereby size reduction during

scale up was maintained by keeping the surface area to void volume ratio

of the elements constant. This was done by addition of more cross bars

for larger diameter elements.

Finally, a simple model relating D43 to capillary number was proposed (by Dr.

Baird). The model is based on equating the work done in breaking a primary

drop by hydrodynamic forces to the increase in surface energy of the drops. It

was found to fit the data reasonably well, and it could prove to be a promising

starting point for more detailed analysis that would take into account the effect

of dispersed phase viscosity and holdup. The model was qualitatively supported

by limited data from a smaller SMX cartridge (15.75 mm diameter)


64

5.2 Recommendations for future work

Based on the experience from conducting the experiments, the following

suggestions are made to improve the experimental apparatus and the flow

visualization/image acquisition system-

Use of high speed cameras and large aperture zoom lens to get high

quality images (without motion blur) with crisp images at high flow rates.

This will aid in increasing the recall and precision of the algorithm in these

cases

Inclusion of a recycling line (by means of a 3-way valve) from the

separating tank for the continuous phase to avoid manual reloading of

the continuous phase tank

Recommendations for further studies are as follows-

Identification of droplet breakup mechanisms further up the packing-by

taking images of its interiors- for different viscosity ratios and surfactant

concentrations

Validations of the influence of the gaps between adjacent plates in the

packing, by possibly altering the number of cross bars in its geometry, or

by carrying out detailed experiments with different sizes of SMX

cartridge.


65

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Appendix A Tabulated Experimental Data

A1

Note: The tabulated data below was used in the Result and Discussion section

Capillary number defined as

Run #

Cell

Diameter

(m)

No.

Elements

c

(Pa.S)

d

(Pa.S) p

(N/m)

qc

(m3/sec)

qd

(m3/sec)

ucd

(m/sec) h RecdCa

D43

(mm)

Dmax

(mm)

1 4.12E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 1.02E-05 5.00E-06 1.14E-02 0.33 8.66 1.99E-02 3.39 5.44

2 4.12E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 3.55E-05 6.50E-06 3.15E-02 0.15 23.98 5.52E-02 2.95 5.23

3 4.12E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 6.83E-05 1.77E-05 6.46E-02 0.21 49.11 1.13E-01 2.36 1.89

4 4.12E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 1.20E-04 1.30E-05 9.97E-02 0.10 75.85 1.75E-01 1.89 5.58

5 4.12E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 1.46E-04 3.07E-05 1.33E-01 0.17 100.98 2.32E-01 1.43 4.86

6 1.58E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 1.03E-05 1.67E-06 6.16E-02 0.14 17.92 1.08E-01 0.99 4.86

7 1.58E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 1.72E-05 2.33E-06 1.00E-01 0.12 29.11 1.75E-01 0.77 4.86

8 1.58E-02 10 7.00E-02 4.89E-01 7.0 4.00E-02 1.58E-05 2.33E-06 9.32E-02 0.13 27.12 1.63E-01 0.72 4.86

9 4.12E-02 6 7.80E-02 4.89E-01 6.3 4.00E-02 1.13E-05 4.50E-06 1.19E-02 0.28 8.11 2.32E-02 3.85 4.86

10 4.12E-02 6 7.80E-02 4.89E-01 6.3 4.00E-02 3.65E-05 6.50E-06 3.23E-02 0.15 22.04 6.30E-02 3.47 5.44

11 4.12E-02 6 7.80E-02 4.89E-01 6.3 4.00E-02 6.92E-05 1.77E-05 6.52E-02 0.20 44.50 1.27E-01 2.94 5.26

12 4.12E-02 6 7.80E-02 4.89E-01 6.3 4.00E-02 1.22E-04 1.30E-05 1.01E-01 0.10 69.01 1.97E-01 2.43 4.46

13 4.12E-02 6 7.80E-02 4.89E-01 6.3 4.00E-02 1.75E-04 7.83E-06 1.38E-01 0.04 93.87 2.68E-01 2.15 3.82

14 4.12E-02 6 2.50E-02 4.89E-01 19.6 4.00E-02 3.87E-05 1.73E-05 4.20E-02 0.31 89.40 2.62E-02 3.52 5.53

15 4.12E-02 6 2.50E-02 4.89E-01 19.6 4.00E-02 6.32E-05 1.33E-05 5.74E-02 0.17 122.31 3.59E-02 3.50 5.49

16 4.12E-02 6 2.50E-02 4.89E-01 19.6 4.00E-02 8.67E-05 2.33E-05 8.25E-02 0.21 175.74 5.16E-02 3.13 5.25

17 4.12E-02 6 2.50E-02 4.89E-01 19.6 4.00E-02 1.13E-04 1.43E-05 9.59E-02 0.11 204.12 5.99E-02 3.12 4.77

18 4.12E-02 6 2.50E-02 4.89E-01 19.6 4.00E-02 1.42E-04 7.42E-06 1.12E-01 0.05 239.43 7.03E-02 2.89 4.79

19 4.12E-02 10 2.50E-02 4.89E-01 19.6 4.00E-02 3.65E-05 1.77E-05 4.07E-02 0.33 86.61 2.54E-02 3.14 5.23

20 4.12E-02 10 2.50E-02 4.89E-01 19.6 4.00E-02 6.60E-05 1.30E-05 5.93E-02 0.16 126.31 3.71E-02 3.14 5.95

21 4.12E-02 10 2.50E-02 4.89E-01 19.6 4.00E-02 7.30E-05 2.30E-05 7.21E-02 0.24 153.49 4.50E-02 2.89 4.65

A2

Run #

Cell

Diameter

(m)

No.

Elements

c

(Pa.S)

d

(Pa.S) p

(N/m)

qc

(m3/sec)

qd

(m3/sec)

ucd

(m/sec) h Recd Ca

D43

(mm)

Dmax

(mm)

22 4.12E-02 10 2.50E-02 4.89E-01 19.6 4.00E-02 1.43E-04 7.67E-06 1.13E-01 0.05 241.43 7.09E-02 2.62 4.11

23 4.12E-02 10 2.50E-02 4.89E-01 19.6 4.00E-02 1.10E-04 1.43E-05 9.34E-02 0.12 198.79 5.83E-02 2.39 4.47

24 4.12E-02 10 2.45E-01 4.89E-01 2.0 4.00E-02 4.74E-05 1.16E-05 4.43E-02 0.20 9.63 2.71E-01 0.89 1.82

25 4.12E-02 10 2.45E-01 4.89E-01 2.0 4.00E-02 4.96E-05 8.25E-06 4.34E-02 0.14 9.44 2.66E-01 0.90 1.75

26 4.12E-02 10 2.45E-01 4.89E-01 2.0 4.00E-02 5.58E-05 3.50E-06 4.45E-02 0.06 9.68 2.73E-01 1.02 1.66

27 4.12E-02 10 2.30E-01 9.78E-01 4.3 4.00E-02 4.57E-05 4.50E-06 3.77E-02 0.09 8.72 2.17E-01 2.07 3.67

28 4.12E-02 10 2.30E-01 9.78E-01 4.3 4.00E-02 6.67E-05 7.83E-06 5.59E-02 0.11 12.95 3.22E-01 1.46 2.80

29 4.12E-02 10 2.30E-01 9.78E-01 4.3 4.00E-02 9.33E-05 1.03E-05 7.78E-02 0.10 18.02 4.48E-01 0.94 1.89

31 4.12E-02 10 2.30E-01 9.78E-01 4.3 4.00E-02 1.18E-04 1.16E-05 9.70E-02 0.09 22.46 5.58E-01 0.69 1.31

32 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 8.23E-05 3.83E-06 6.47E-02 0.04 44.16 1.26E-01 2.52 4.23

33 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 7.50E-05 8.33E-06 6.26E-02 0.10 42.71 1.22E-01 2.41 4.03

34 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 7.30E-05 1.30E-05 6.46E-02 0.15 44.07 1.26E-01 2.25 4.30

35 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 6.92E-05 1.63E-05 6.42E-02 0.19 43.82 1.25E-01 2.25 3.53

36 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 1.04E-04 1.10E-05 8.61E-02 0.10 58.76 1.68E-01 2.10 3.94

37 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 1.36E-04 1.43E-05 1.13E-01 0.10 76.91 2.20E-01 1.73 3.44

38 4.12E-02 10 7.80E-02 9.78E-01 12.5 4.00E-02 3.67E-05 3.83E-06 3.04E-02 0.09 20.75 5.93E-02 3.20 5.55

39 4.12E-02 10 2.70E-02 9.78E-01 36.2 4.00E-02 5.33E-05 6.50E-06 4.49E-02 0.11 88.58 3.03E-02 3.63 5.58

40 4.12E-02 10 2.70E-02 9.78E-01 36.2 4.00E-02 7.77E-05 8.83E-06 6.49E-02 0.10 128.06 4.38E-02 3.30 5.38

41 4.12E-02 10 2.70E-02 9.78E-01 36.2 4.00E-02 1.02E-04 1.20E-05 8.53E-02 0.11 168.28 5.76E-02 3.06 4.61

42 4.12E-02 10 2.70E-02 9.78E-01 36.2 4.00E-02 1.30E-04 1.48E-05 1.09E-01 0.10 214.42 7.34E-02 2.65 4.20

43 4.12E-02 10 2.70E-02 9.78E-01 36.2 4.00E-02 6.67E-05 1.77E-05 6.33E-02 0.21 124.85 4.27E-02 3.20 5.58

44 4.12E-02 10 2.70E-02 9.78E-01 36.2 2.30E-02 5.67E-05 6.50E-06 4.74E-02 0.10 93.51 5.57E-02 3.39 4.84

45 4.12E-02 10 2.70E-02 9.78E-01 36.2 2.30E-02 9.58E-05 8.83E-06 7.86E-02 0.08 154.95 9.23E-02 2.90 4.28

A3

Run #

Cell

Diameter

(m)

No.

Elements

c

(Pa.S)

d

(Pa.S) p

(N/m)

qc

(m3/sec)

qd

(m3/sec)

ucd

(m/sec) h Recd Ca

D43

(mm)

Dmax

(mm)

46 4.12E-02 10 2.70E-02 9.78E-01 36.2 2.30E-02 1.15E-04 1.15E-05 9.50E-02 0.09 187.28 1.11E-01 2.60 4.87

47 4.12E-02 10 2.70E-02 9.78E-01 36.2 2.30E-02 1.41E-04 1.50E-05 1.17E-01 0.10 230.70 1.37E-01 2.30 4.41

48 4.12E-02 10 2.70E-02 9.78E-01 36.2 2.30E-02 6.13E-05 6.50E-06 5.09E-02 0.10 100.42 5.98E-02 3.19 4.72

49 4.12E-02 10 2.70E-02 9.78E-01 36.2 2.30E-02 2.50E-05 6.50E-06 2.37E-02 0.21 46.63 2.78E-02 3.37 4.86

53 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 2.50E-05 5.00E-06 2.25E-02 0.17 44.41 2.64E-02 3.41 5.09

54 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 1.13E-04 1.30E-05 9.49E-02 0.10 187.03 1.11E-01 2.18 4.13

55 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 8.50E-05 8.83E-06 7.05E-02 0.09 138.91 8.27E-02 2.60 4.41

56 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 1.48E-04 1.63E-05 1.24E-01 0.10 243.78 1.45E-01 1.88 3.57

57 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 5.83E-05 6.50E-06 4.87E-02 0.10 95.98 5.71E-02 2.92 5.09

58 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 9.00E-05 4.17E-06 7.07E-02 0.04 139.41 8.30E-02 2.38 4.31

59 4.12E-02 10 2.70E-02 4.89E-01 18.1 2.30E-02 7.67E-05 1.50E-05 6.88E-02 0.16 135.71 8.08E-02 2.70 4.72

60 4.12E-02 10 7.40E-02 4.89E-01 6.6 2.30E-02 6.68E-05 6.50E-06 5.51E-02 0.09 39.61 1.77E-01 2.12 3.88

61 4.12E-02 10 7.40E-02 4.89E-01 6.6 2.30E-02 3.05E-05 3.33E-06 2.54E-02 0.10 18.28 8.17E-02 2.57 4.53

62 4.12E-02 10 7.40E-02 4.89E-01 6.6 2.30E-02 1.02E-04 1.00E-05 8.38E-02 0.09 60.32 2.70E-01 1.54 3.18

64 4.12E-02 10 7.40E-02 4.89E-01 6.6 2.30E-02 1.43E-04 1.53E-05 1.19E-01 0.10 85.71 3.83E-01 1.12 2.33

65 4.12E-02 6 7.40E-02 4.89E-01 6.6 2.30E-02 1.02E-04 1.12E-05 8.47E-02 0.10 60.95 2.73E-01 1.89 3.29

66 4.12E-02 6 7.40E-02 4.89E-01 6.6 2.30E-02 1.37E-04 1.50E-05 1.14E-01 0.10 81.92 3.66E-01 1.46 3.01

67 4.12E-02 6 7.40E-02 4.89E-01 6.6 2.30E-02 6.00E-05 7.67E-06 5.08E-02 0.11 36.55 1.63E-01 2.85 4.97

68 4.12E-02 6 7.40E-02 4.89E-01 6.6 2.30E-02 2.83E-05 3.33E-06 2.38E-02 0.11 17.11 7.65E-02 3.41 5.21

69 4.12E-02 6 7.40E-02 4.89E-01 6.6 2.30E-02 7.75E-05 8.33E-06 6.44E-02 0.10 46.36 2.07E-01 2.65 4.66

71 4.12E-02 10 7.40E-02 9.78E-01 13.2 2.30E-02 3.28E-05 3.58E-06 2.73E-02 0.10 19.67 8.80E-02 3.21 5.37

72 4.12E-02 10 7.40E-02 9.78E-01 13.2 2.30E-02 6.27E-05 7.42E-06 5.26E-02 0.11 37.86 1.69E-01 2.67 4.78

73 4.12E-02 10 7.40E-02 9.78E-01 13.2 2.30E-02 8.03E-05 8.67E-06 6.68E-02 0.10 48.07 2.15E-01 2.52 4.32

A4

Run #

Cell

Diameter

(m)

No.

Elements

c

(Pa.S)

d

(Pa.S) p

(N/m)

qc

(m3/sec)

qd

(m3/sec)

ucd

(m/sec) h RecdCa

D43

(mm)

Dmax

(mm)

74 4.12E-02 10 7.40E-02 9.78E-01 13.2 2.30E-02 1.49E-04 1.43E-05 1.23E-01 0.09 88.32 3.95E-01 2.18 4.08

75 4.12E-02 10 7.40E-02 9.78E-01 13.2 2.30E-02 1.03E-04 1.30E-05 8.68E-02 0.11 62.48 2.79E-01 2.27 4.11

76 4.12E-02 10 7.40E-02 9.78E-01 13.2 2.30E-02 1.34E-04 1.38E-05 1.11E-01 0.09 79.58 3.56E-01 2.27 4.06

77 4.12E-02 10 2.30E-01 9.78E-01 4.3 2.30E-02 4.57E-05 4.50E-06 3.77E-02 0.09 8.72 3.77E-01 1.78 3.30

78 4.12E-02 10 2.30E-01 9.78E-01 4.3 2.30E-02 7.30E-05 7.67E-06 6.06E-02 0.10 14.02 6.06E-01 1.16 2.29

79 4.12E-02 10 2.30E-01 9.78E-01 4.3 2.30E-02 9.69E-05 1.00E-05 8.03E-02 0.09 18.58 8.03E-01 0.82 1.86

80 4.12E-02 10 2.30E-01 9.78E-01 4.3 2.30E-02 1.14E-04 1.30E-05 9.52E-02 0.10 22.04 9.52E-01 0.61 1.44

81 4.12E-02 10 2.30E-01 9.78E-01 4.3 2.30E-02 2.83E-05 3.33E-06 2.38E-02 0.11 5.50 2.38E-01 1.97 3.55

82 4.12E-02 10 2.30E-01 9.78E-01 4.3 1.30E-02 2.89E-05 3.58E-06 2.44E-02 0.11 5.65 4.32E-01 1.55 3.17

83 4.12E-02 10 2.30E-01 9.78E-01 4.3 1.30E-02 4.83E-05 5.00E-06 4.00E-02 0.09 9.27 7.08E-01 1.27 2.42

84 4.12E-02 10 2.30E-01 9.78E-01 4.3 1.30E-02 7.00E-05 7.17E-06 5.79E-02 0.09 13.41 1.03E+00 0.76 1.47

85 4.12E-02 10 2.30E-01 9.78E-01 4.3 1.30E-02 9.50E-05 6.50E-06 7.62E-02 0.06 17.64 1.35E+00 0.44 0.85

87 4.12E-02 10 6.00E-02 9.78E-01 16.3 1.30E-02 2.17E-05 3.33E-06 1.88E-02 0.13 16.65 8.66E-02 2.45 4.10

88 4.12E-02 10 6.00E-02 9.78E-01 16.3 1.30E-02 7.11E-05 8.83E-06 6.00E-02 0.11 53.24 2.77E-01 2.00 3.89

89 4.12E-02 10 6.00E-02 9.78E-01 16.3 1.30E-02 4.87E-05 5.00E-06 4.03E-02 0.09 35.75 1.86E-01 2.20 3.85

91 4.12E-02 10 6.00E-02 9.78E-01 16.3 1.30E-02 1.01E-04 1.15E-05 8.41E-02 0.10 74.61 3.88E-01 1.97 3.74

92 4.12E-02 10 6.00E-02 9.78E-01 16.3 1.30E-02 1.27E-04 1.43E-05 1.06E-01 0.10 93.93 4.89E-01 1.37 2.65

93 4.12E-02 10 6.00E-02 4.89E-01 8.2 1.30E-02 2.50E-05 3.58E-06 2.15E-02 0.13 19.04 9.91E-02 2.33 4.06

94 4.12E-02 10 6.00E-02 4.89E-01 8.2 1.30E-02 4.99E-05 7.17E-06 4.29E-02 0.13 38.03 1.98E-01 1.87 3.47

95 4.12E-02 10 6.00E-02 4.89E-01 8.2 1.30E-02 7.17E-05 7.08E-06 5.91E-02 0.09 52.46 2.73E-01 1.67 2.90

96 4.12E-02 10 6.00E-02 4.89E-01 8.2 1.30E-02 1.01E-04 1.16E-05 8.42E-02 0.10 74.67 3.88E-01 1.50 2.55

Appendix B Code in Visual C++ with OpenCV library

B1

//The following code was used for image processing and has been

explained in the experimental section (section 3.4)

#include "stdafx.h"

#include <cv.h>

#include <cxcore.h>

#include <highgui.h>

#include <math.h>

#include <sstream>

#include <iostream>

#include <fstream>

#include <stdio.h>

#include <stdlib.h>

using namespace std;

cvHoughCircles_2( CvArr* src_image, void* circle_storage,

int method, double dp, double min_dist,

double param1, double param2,

int min_radius, int max_radius, int circles_max );

int _tmain(int argc, _TCHAR* argv[])

{

IplImage *image,*e,*contour;

const char *c_filename, *c_filename_output;

string filename, filename_output;

string

string1="run87/run87_0",string2="_output",string3="run87/run87_000

",string4="run87/run87_00";

int frame;

string s;

stringstream out;

ofstream myfile;

//output file for radius vector

myfile.open("run87/output_run87.txt");

for(frame=1; frame<=200; frame++)

{

out<<frame;

s=out.str();

if(frame<10){

filename=string3+s+".bmp";

}

else if(frame<=99){


}

else {


B2

}

c_filename=filename.c_str();

image =

cvLoadImage(c_filename,CV_LOAD_IMAGE_GRAYSCALE);

e = cvCloneImage(image);

//bilateral smoothing

cvSmooth(image,e,CV_BILATERAL,11,11,100,5);

cvWaitKey(0);

CvMemStorage* storage = cvCreateMemStorage(0);

//Hough transform for small radii

CvSeq* results1 = cvHoughCircles_2(e,

storage,

CV_HOUGH_GRADIENT,

2,

100,

22,

150,

18,

99,

12);//threshold was 75//Canny for big mixer was 40//

//Hough transform for large radii

CvSeq* results2 = cvHoughCircles_2(e,

storage,

CV_HOUGH_GRADIENT,

2,

150,

22,

220,

100,

310,

10);//thershold was 160//Canny for big mixer was 50*/

//output results in the text file and mark indentifed

circles

for( int i = 0; i < results1->total; i++ ) {

float* p = (float*) cvGetSeqElem( results1, i );

CvPoint pt = cvPoint( cvRound( p[0] ), cvRound(

p[1] ) );

myfile<<cvRound(p[2])<<"\n";

B3

cvCircle(

image,

pt,

cvRound( p[2] ),

CV_RGB(0xff,0xff,0xff),

6

);

}

for( int i = 0; i < results2->total; i++ ) {

float* p = (float*) cvGetSeqElem( results2, i );

CvPoint pt = cvPoint( cvRound( p[0] ), cvRound(

p[1] ) );

myfile<<cvRound(p[2])<<"\n";

cvCircle(

image,

pt,

cvRound( p[2] ),

CV_RGB(0xff,0xff,0xff),

6

);

}

filename_output=string1+s+string2+".jpg";

c_filename_output=filename_output.c_str();

cvSaveImage(c_filename_output,image);

cvReleaseImage(&image);

cvReleaseImage(&e);

s.clear();

out.str(string());

}

myfile.close();

}

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